Arsen Avakov said that a "column" with armoured vehicles crossed from Russia through border control points controlled by pro-Russian separatists near the Dyakove village in eastern Ukraine, according to the Interfax news agency.

Mr Avakov said that "part of this column has been destroyed" by Ukrainian forces.

He said the incursion took place despite Russian statements of interest in a peaceful solution and intent to increase border controls.

The reports followed statements by Russia's foreign minister that the pro-Moscow separatist rebels in eastern Ukraine are ready for a ceasefire but that Kiev has to initiate the process.

Sergey Lavrov was also quoted by Russian news agencies as saying Moscow will introduce a resolution in the United Nations on the Ukrainian crisis, but that Russia was not seeking authorisation to send in peacekeeping troops.

The Ukrainian rebels have suggested that Russia should send peacekeepers, but Moscow says that could only be done with UN authorisation.

Ukraine's government and Western countries allege that Russia is fomenting or supporting the uprising in the east, where insurgents have declared two regions independent and are seeking annexation by Russia.

Moscow denies it has agents in eastern Ukraine, but it is unclear to what extent it has contacts or influence with the rebels.

Mr Lavrov said: "We know that the rebels in the south-east are ready to hold fire, but the first step by all rights should be made by the Kiev authorities."

He said the proposed UN resolution would concentrate on demanding fulfilment of proposals set forth in a so-called "road map" for resolving the conflict developed by the Organisation of Security and Cooperation in Europe (OSCE).

The OSCE's secretary-general today visited a camp in Russia for refugees from the conflict in Ukraine's east and called for the fighting to end.

According to the Interfax news agency, Lamberto Zannier said that the conflict in the east "is craziness which must be stopped".

Russia says some 30,000 people have fled the fighting.

Ukraine's new president, Petro Poroshenko, this week called for the establishment of safe-passage corridors for civilians who want to escape the violence in the east, but no visible steps towards creating them have been seen.